WHEN YOU SHARE something about Islam with a non-Muslim and you get resistance, respond with something like this: "Well, tell me what you've learned about Islam so far. Let's start there." Ask the question in a casual, relaxed, easygoing, not-in-the-slightest-bit-defensive way. Practice asking that question when you're alone, so you can deliver it perfectly and with just the right tone.
And after you ask the question, listen. Let the person speak until they're done.
When they finish, tell them what you have found out. Take something specific, and say, "I used to think exactly the same thing until I read the Koran. And what I found out really surprised me..."
A back-and-forth argument usually doesn't change anyone's mind, and tends to create negative feelings. But the kind of conversation you get with the approach above has a chance of making your listener consider what you have to say, which could lead to them changing their mind eventually.